Multiple germanium atom quantum dot and devices inclusive thereof

ABSTRACT

A multiple-atom germanium quantum dot is provided that includes multiple dangling bonds on an otherwise H-terminated germanium surface, each dangling bonds having one of three ionization states of +1, 0 or −1 and corresponding respectively to 0, 1, or 2 electrons in a dangling bond state. The dangling bonds together in close proximity and having the dangling bond states energetically in the germanium band gap with selective control of the ionization state of one of the dangling bonds. A new class of electronics elements is provided through the inclusion of at least one input and at least one output to the multiple dangling bonds. Selective modification or creation of a dangling bond is also detailed.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/318,626, filed Jan. 17, 2019; now U.S. Pat. No. ______; which in turnis a US National Phase Application of PCT/IB2017/001051, filed Jul. 19,2017; which in turn claims priority benefit of U.S. Provisional PatentApplication Ser. No. 62/364,206. filed Jul. 19, 2016; and U.S.Provisional Patent Application Ser. No. 62/379,164, filed Aug. 24, 2016;the contents of which are all hereby incorporated herein by reference.

FIELD OF THE INVENTION

The present invention is directed generally to multiple dangling bonds(DBs) on an otherwise H-terminated silicon surface that form quantumdots and in particular to devices based on the modulation of theoccupation state of a DB on such a quantum dot.

BACKGROUND

Using scanning probe microscopy techniques, inducing and visualizingchemical reactions at the atomic scale is routinely achievable. In theframework of so-called mechanochemistry, (1) mechanical force inducedreactions have been studied using NCAFM. (2) Recent works reported forceinduced atomic-scale switching, (3) quantitative force measurements toinduce the diffusion of single atoms (4) and molecules, (5) as well asstudying molecular conformers (6) and tautomerization. (7) Other studieshave shown examples of mechanically induced vertical manipulation ofsingle atoms. (8, 9) However, direct observation of mechanically inducedcovalent bonding of two different atoms using NC-AFM remain scarce. (10)

Recently, the silicon dangling bond (DB) on the technologically relevantH—Si(100) surface was established as a very promising building block forbeyond CMOS technology.(11, 12) A DB corresponds to a desorbed singlehydrogen atom from the otherwise passivated silicon surface. It isapproximately an sp3 hybrid orbital that can be occupied by 2, 1, or 0electrons resulting, respectively, in a negative, neutral, or positivelycharged DB. Thus, a DB behaves essentially as a single atom quantum dot,with charge state transitions reported in STM experiments.(13, 14) DBscan be found natively on the surface as a result of imperfections duringthe hydrogen termination procedure or artificially created using the STMtip. Different works have shown that controlled atom-by-atomlithography, i.e. hydrogen desorption, on the H—Si surface allowscreation of DB based circuits for next generation ultimatelyminiaturized low power nanoelectronic devices. (11, 12, 15-17)

Although STM tip induced desorption of hydrogen from the H—Si(100)surface has been extensively studied,(16, 18-23) the reversemanipulation of selective adsorption of a single hydrogen atom topassivate a silicon DB remains to be explored. In this context, AFM canbring more insights by allowing identification of different tip dynamics(24, 25) and probing chemical reactivity at the atomic scale. (26, 27)

The promise of atom scale computing first became a possibility whenEigler et al. controllably moved atoms on a surface to achievestructures of their design (1). In a subsequent work, the same lab mademolecular cascades where, in analogy to falling dominoes, a terminalmolecule was tipped to, in turn, tip over a neighboring molecule, whichtipped the next molecule, and so on (2). Separate branches of thecascade were delicately timed to come together in such a way as toachieve binary logic functions. With these results a new era was begun.However, challenges preventing practical applications remained and thoselimitations have been very difficult to overcome. Some of thosechallenges are; 1) the need to have the patterned atoms be robust atpractical operation temperatures ideally room temperature. The initialatomic patterns were very delicately bound and would not persist aboveabout −250° C. (1, 2). In general, atom fabrication of structures robustenough to withstand relatively high operating temperature are moredifficult to make. This is because larger energy inputs from the scannedprobe are required to dislodge and move strongly bound atoms, and undersuch conditions covalent bonds within the probe itself break with someprobability comparable to that of the target bond (3). 2) The patternedatoms need to be electrically distinct from the substrate so as toenable conduction pathways that are not shorted-out or altered by thesubstrate. Studies performed on metals (4, 5), the most common choice,were therefore limited in that regard. Isolation has been achieved instudies of metal atoms and of molecules separated from a metal substrateby a salt layer, but these have their limitations in uniformity of layerthickness and issues with spontaneous loss of charge to the substrate(6, 7). 3) The atomic circuitry must not require mechanical or otherreset processes (analogous to standing all the dominoes back up) thatwould prevent the circuitry being instantly reusable.

SUMMARY OF THE INVENTION

A multiple-atom silicon quantum dot is provided that includes multipledangling bonds on an otherwise H-terminated silicon surface, eachdangling bonds having one of three ionization states of +1, 0 or −1 andcorresponding respectively to 0, 1, or 2 electrons in a dangling bondstate. The dangling bonds together in close proximity and having thedangling bond states energetically in the silicon band gap withselective control of the ionization state of one of the dangling bonds.A new class of electronics elements is provided through the inclusion ofat least one input and at least one output to the multiple danglingbonds. Selective modification or creation of a dangling bond is alsodetailed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a 3DB Chain. (a,b) STM constant current images at −1.8V and1.4V respectively. The current setpoint was 50 pA. (c-e) dI/dV mapstaken at a tip height of −1.8V, 20 pA with a 60 pm tip retraction overan H—Si dimer. The sample bias during collection of each dI/dV map islabelled in the upper left corner of the map. The scale bar for the STMimages and the dI/dV maps is shown in (a). (f) dI/dV line scans atvarying energy along the 3 nm dotted line overlaid on the STM image (a).

FIG. 2 shows a DB Chains of greater length. (a) 4DB Chain, (b) 5DBChain, (c) 6DB Chain, (d) 7DB Chain. The 5DB (b) and 6DB (c) Chains wereformed by adding DBs to the upper right end of the 4DB chain (a). Thefirst image of each column is an STM constant current image at −1.8V, 50pA. All other images are dI/dV maps taken at a tip height of −1.8V, 20pA with a 60 pm tip retraction over an H—Si region. The sample biasduring collection of each dI/dV map is labelled in the upper left cornerof the map. The scale bar for both the STM image and the dI/dV maps foreach column is shown at the bottom of each column's STM image.

FIG. 3 shows a controlled perturbation of a 7DB chain (a) with a singleDB (b) and with a bare dimer (c). The top images in (a-c) are STMconstant current images taken at −1.8V with a current setpoint of 50 pA.The bottom images are dI/dV linescans of the 7DB chain and theperturbing feature along the central axis of the 7DB chain, shown in thedotted line overlaid on the STM image in (a). The height setpoint of thedI/dV linescans was −1.8V, 20 pA with a tip retraction of 60 pm over aH—Si dimer. The x scale of each dI/dV linescan is lined up with the xscale of each STM image. The perturbing single DB in (b) is located onthe same side of the dimer row as the 7DB chain, with one interveningH—Si dimer between the DB and the 7DB chain. The perturbing bare dimerin (c) was made by removing the DB on the same dimer as the originalperturbing DB in (b). In all dI/dV linescans, the state densityassociated with the 7DB chain is found at an x position of 1 nm to 4.5nm. In the dI/dV linescans of (b) and (c), the state density of thesingle DB and the bare dimer respectively are found at an x position of˜5.5 nm.

FIG. 4 shows a graph. The graph at the right of FIG. 4 shows colourcoded curves of change in atomic force microscopy oscillation frequencyas a function of applied voltage between probe and sample. Thepronounced transitions represent the charge state transition of theparticular DB beneath the probe. The normally transition of ˜−0.2 isgreatly shifted for the most perturbed DB and in a sense consistent withthe negative charged perturbation.

FIG. 5 shows an elaboration of FIG. 4 depicting two qubits. When thesame perturbation of FIG. 4 are applied—the same result was achieved inthe nearest qubit. Remarkably, in addition, it is observed that thequbit directly biased by the perturber has in turn biased the secondqubit. Note the most perturbed DBs are still present but rendered herealmost invisible. These electronic changes are entirely reversible.

FIGS. 6A-6D show Probing charge State Transition in an AtomicSiliconQuantum Dot using NC-AFM. FIG. 6A shows a 3×3 nm filled statesSTM image (−1.7 V and 50 pA) and FIG. 6B corresponding frequency shiftmap at 0 V of an ASiQD (zrel=−350 p.m and Amp=100 p.m). FIG. 6C showsCurrent vs. Bias spectroscopy plotted in log scale of the ASiQD (black)and hydrogen terminated surface (red). FIG. 6D shows frequency shift asa function of voltage measured above the ASiQD.

FIGS. 7A-7I show the polarization effect on a multiple Atomic SiliconQuantum dots structure. STM images (−1.8 V and 50 pA), frequency shiftmaps (zrel=−380 p.m and Amp=100 p.m) and frequency shift versus biasspectra (Δf (V)) for a single ASiQD (FIGS. 7A-7C), 2 tunnel coupledASiQDs (FIGS. 7D-7F), and a 2+1 structure (FIGS. 7G-7I). The Δf (V)spectra are color-coded according to the arrows in AFM images.

FIGS. 8A-8F show information transmission through atomic silicon quantumdot (ASiQD) constructed binary wire. FIG. 8A shows Filled states STMimage and FIG. 8B corresponding frequency shift maps of a 17 ASiQD wire.Color guides are placed in FIG. 8B to show the location of the dots.FIG. 8C shows symmetric 18 atom ASiQD wire creating from adding on theright of FIG. 8A. FIG. 8D is a frequency shift map of the dots showingthe symmetry splitting plane marked by the dashed white line FIG. 8E 19atom wire with symmetry broken by adding a ASiQD on the left. FIG. 8F isa frequency shift map showing the wire polarized to the right. All STMimages were taken at V −1.7 and 50 pA. All AFM images were taken at 0 V,with a relative tip elevation of z=330 p.m and an oscillation amplitudeof 0.5° A.

FIGS. 9A-9O show examples of a functional OR gate constructed usingatomic silicon quantum dots (ASiQD). FIGS. 9A, 9D, 9G, 9J, and 9M showconstant current filled states STM images (−1.8V, 50 pA) of the OR gate,and FIGS. 9B, 9E, 9H, 9K, and 9N show the corresponding frequency shiftmaps (0V, Z 3.5 A°). FIG. 9C shows the truth table of an OR gate, whileFIGS. 9F, 9I, 9L, and 9O show models for the switching inputs andoutputs corresponding to the various gate states displayed.

FIGS. 10A-10D show illustrations of the tip induced manipulation thatcan result in tip functionalization with a single hydrogen atom. FIG.10A shows a ball and stick model of the H—Si(100)-2×1 surface. FIG. 10Bshows typical defect-free empty states STM image using anon-functionalized tip and showing the dimer structure of the surface.The red dot indicates the position of the STM tip when the electronicexcitation sketched in FIG. 10A is applied. FIG. 10C shows a ball andstick model of a silicon dangling bond in green and a H-functionalizedtip resulting from the tip-induced desorption. FIG. 10D shows typicalSTM image of a DB acquired with a H-functionalized tip showing acharacteristic STM contrast enhancement. Both STM images were acquiredin constant current mode with a set point of 50 pA at +1.3 V.

FIGS. 11A-11D show imaging of a single hydrogen atom physisorbed on theHSi(100) surface. FIG. 11A shows a (5×5)nm² STM image at +1.3 V of a DBwhere the desorbed atomic hydrogen was not picked up, instead adsorbingat the location indicated by an arrow. FIG. 11B shows a (3×3)nm² STMimage of an atomic hydrogen adsorbed on the surface and FIG. 11C shows acorresponding AFM frequency shift map at 0 V and a relative tipelevation of z=−3.8 Å. FIG. 11D shows an atomic hydrogen on the surfaceis picked up by a slow downward STM scan at V=+1.6V. All STM images areconstant current at 50 pA.

FIGS. 12A-12F show a procedure to mechanically induce a hydrogen-siliconcovalent bond. FIG. 12A shows a typical filled states STM image of asilicon dangling bond on the H—Si(100)-2×1 surface using a singlehydrogen atom functionalized tip. The yellow arrow indicates a defecttaken as a reference. FIG. 12B shows a Δf(z) curve usingH-functionalized tip on a surface hydrogen atom. FIG. 12C shows a balland stick model and FIG. 12D shows a Δf(z) curve on a single DB duringthe mechanically induced Si—H covalent bond capping event. The orangearrow indicates a hysteresis (zoom in inset) characteristic of thechange that occurs due to the formation of the covalent bond between theH atom at the tip apex and the silicon dangling bond. FIG. 12E shows aSTM image and FIG. 12F shows a Δf(z) curve on the H—Si surfacesubsequent to the mechanically induced reaction in FIG. 12D.

FIGS. 13A-13C show NC-AFM characterization of a single DB on theHSi(100)-2×1 surface using a H-functionalized tip. FIG. 13A shows aΔf(z) curves recorded on the H—Si surface (blue curve) and on thesilicon DB (red curve). (3×3)nm² frequency shift maps of a DB on theH—Si surface at relatively large FIG. 13B and small FIG. 13C tip-sampledistances respectively. All data was acquired at 0 V with an oscillationamplitude of 1 Å.

FIGS. 14A-14H show altering coupling and artificial molecular orbitalsin multi-DB structures. FIG. 14A shows two pairs of coupled DBs on theH—Si(100) surface arranged along a same dimer row. FIG. 14B shown animage of the same area after the mechanically induced capping of the farright DB in FIG. 14A. 14C shows a (3×2)nm² STM image of threetunnel-coupled DBs. FIG. 14B shows the same area after erasing themiddle DB in FIG. 14C. Constant current images FIGS. 14A-14D wereacquired at −1.8 V and 50 pA. FIGS. 14E-14F shows Willed (−2.0 V, 50 pA)and FIGS. 14g -14H show empty (+1.4 V, 50 pA) states STM images of a DBwire, respectively, before and after erasing the far right DB in FIG.14E. 3d models of the four (FIG. 14I) and three (FIG. 14J) DB wire.Positions of erased DBs are indicated by dotted circles.

FIG. 15A shows that a single hydrogen atoms physisorbed on thechemically inert H—Si(100) surface could be stably imaged in filledstates at low voltage (+1.3 V). However, when the scanning voltage isincreased to +1.7V in (b), the hydrogen atom is dragged by the tip whichresulted in the capping of the DB during the STM image as indicated by achange in contrast midway through the image and confirmed by asubsequent STM image of the same area as shown in FIG. 15C. FIGS. 15Band 15C are larger area (10×10)nm²) images of the area in FIG. 15A. Thelocation of the atomic hydrogen is marked with an arrow.

FIGS. 16A-16E show a series of raw (3×3)nm² NC-AFM frequency shift mapsof H—Si(100) surface at different tip-sample elevations. Images wererecorded at 0 V and with an oscillation amplitude of 1 Å. FIGS. 16A-16Eshow the evolution from atomic to chemical bond contrast on the H—Sisurface. For smaller tip elevations, much higher interaction force isseen on the DB than elsewhere on the surface. Z=0 Å corresponds to thetip position defined by the STM imaging set points (30 pA and +1.3 V)before switching off the feedback loop.

FIG. 17A shows a NC-AFM frequency shift map of a single DB at smalltip-sample distance (˜4.6 Å) and FIG. 17B shows correspondingsimultaneously obtained excitation channel map. FIG. 17C shows asuperposed excitation versus tip elevation curves recorded on the sameDB (red curve) and on the H—Si surface (blue curve).

FIGS. 18A-18D show a method of making and identifying ahydrogen-passivated tip according to the present invention. FIG. 18Ashows a (20×20) nm² constant current (30 pA, −2.0V) STM image of theH—Si surface with a (5×5)nm² bare silicon area appearing as a brightsquare at the center of the image, and obtained with tip-inducedhydrogen desorption. Following tip shaping procedure, the STM imagebecomes very sharp (FIG. 18B) and no longer shows the double tip effectvisible in FIG. 18A. Red arrows indicate the location of the tip-inducedsilicon dimer hydrogen termination. FIGS. 18C and 18D show frequencyshift versus tip-sample distance of a reactive and a passivated tip,respectively.

FIGS. 19A-19H show a series of frequency shift maps at different tipelevations. FIG. 19A shows a ball and stick model showing three siliconlayers of the H—Si surface in the 2×1 reconstruction. FIG. 19B shows a(2×2) nm² constant current (30 pA, +2 V) STM image acquired with apassivated tip. FIG. 19C-H show a series of raw NC-AFM frequency shiftmaps of H—Si surface at different tip elevations. Images are recorded at0V and with an oscillation amplitude of 1 Å.

FIGS. 20A-20C show simulated force maps from DFTB calculations. FIG. 20Ashows a tip structure and H—Si slab considered in the DFTB calculations.FIGS. 20B and 20C show a series of simulated (2×2)nm² force maps atdifferent elevations using a rigid and a flexible tip, respectively.

FIGS. 21A and 21B show simulated force maps for frozen slabs. Partialside view of the frozen slabs (upper panels) along with their simulatedforce maps (lower panels). In a, the dimer hydrogens are fixed in theirrelaxed positions, while in FIG. 21B they are slightly bent and fixed toobtain reverse distances between dimer and interdimer hydrogens withrespect to FIG. 21A.

DESCRIPTION OF THE INVENTION

The present invention has utility as a multi-silicon atom quantum dot(ASiQD) that is a collection of either as close spaced as thecrystalline silicon substrate lattice allows, or with intervening spaceswhich are populated by H atom-terminated surface silicon atoms, to forman elongated, or simply long, quantum dot. The dangling bonds that arethe operational elements of the present invention are not H atomterminated.

It is appreciated that other shapes, any the lattice allows for, canalso be made. These can be termed ASiMs, for atomic silicon molecules.Additional shapes include V-shapes, Y-shapes, triangles, squares, andrectangles.

As used herein, a quantum dot is defined as having collective electronicenergy levels and is an artificial molecule.

The long quantum dot can be a linear arrangement or any other shape thelattice allows. An artificial benzene of ASiQDs has been created. Simplelinear close packed arrangement consisting of 2, 3, 4, 5, 6, 7 ASiQDshave been formed and characterised with dI/dV maps covering a range ofvoltages and a spatial line spanning the length of the molecule.Constant current, constant height and dI/dV over an area larger than themolecule have all been recorded. These images show the spatial andenergetic variations of the collective molecular states of theensembles.

All the attributes of molecules and uses thereof, the inventive ASiMshas like attributes and uses. An inventive ASiM is tailored, and isformed to have specific light absorption and emission properties.

Molecules have the attributes of: being polarized with an electric fieldto exhibit a field distorted electronic structure, being ionized eitherby adding or subtracting electrons, and entering into chemicalreactions. In attributes of ASiMs that allow them to serve as electroniccomponents in classical binary or analog circuitry or as coherentelectron elements with quantum circuitry include: an electric fieldinduced altered electronic structure is used in some inventiveembodiments to convey an action at a distance; a perturbation, or asignal input at one end or region of an ASiM can be registered elsewhereon the ASiM; a receptor or detector of that alteration can effectivelycomplete a transmission of information; and multiple inputs along a ASiMcan diversely and programmatically alter the electronic structure so asto achieve a computation which can be registered by receptors at one ormore other points on the ASiM. Collections of inventive ASiMs, orequivalently, molecules with gaps? spacing, can exhibit profound shiftsin electronic structure in response to perturbations: such molecules canexhibit 2 state binary behavior, or, continuously variable electronicbehavior with a very large polarization range; in a binary application,a linear wire like molecule, or a more complex shape composed of manysuch contiguous line segments, will exhibit two longitudinally shiftedelectronic states, and those can be used to represent, store andtransmit binary information; and in a quantum electronic application,the same structure types as above can couple distant qubits, with eithersign of coupling, in a way known as J coupling. Typically, J couplingrefers to coupling between two spins, such as in an Ising model. Such Jcoupling is analogous to capacitive coupling in an electric circuit andis often referred to as ZZ coupling in the quantum computing literature.Variants on ASiM based couplers also allow inductive-like coupling knownas XX coupling. Other variants too can be made. Access to diverse types,strengths and sign of coupling allows for more diverse, more nearlyuniversal quantum computing.

Fabricating ASiMs where and as needed represents a new, practicalexpression of what has been termed molecular electronics. Unlikeprevious attempts, where molecular chemistry is laborious and mostlyunsuccessfully guided into a desired position, the present inventionachieves positioning and interfacing to wire contacts and othercomponents by making the wire and other components where and as needed.The inventive quantum dots and related interfacial components can betailored so as to have the dimensions, content and properties desired.

An important property of the ASiQDs is that its electronic states are inthe crystalline silicon band gap. Likewise, ASiMs have new collectivestates that are also in the band gap. The splitting associated withbonding among ASiQDs is of order 0.1 eV limiting the molecular states tothe gap region as well.

Crucially, the collective states of the ASiMs therefore do noteffectively mix with silicon bulk electronic states, allowing for atomsized wires and other electric classical and quantum elements to beformed on the silicon surface and be largely electrical insulated anddecoupled from the bulk without the need for an intervening insulator.

The elimination of the need for an insulator enormously reduces thedimensions of a conductor that can be routed over a silicon surface,while also allowing the atom size conductor to be perfectly ordered withrespect to the underlying silicon lattice.

The perfect order and small overall size of such wires and otherelements allows or identical structures to be fabricated. Identicalstructures have homogenous properties. Circuits and devices composed ofelements with homogeneous properties have themselves far morepredictable properties than devices and circuits made of elements with arange of properties.

Single electron transistors can be made of ASiQDs (SEM ASiM). The SEMASiM includes at least two densely packed wire units with one or moreatoms serving as a quantum dot in the centre. SET circuits in the past,made by lithographic techniques, have had such wide variation inproperties among SETs that no circuit built of a collective of suchvariable SETs could practically be made to function. An SET circuitcreated of identical SET ASiMs by contrast, function without the needfor tuning of each and every SET and would therefore be simpler and morecost effective to make and to operate.

ASiM SETs will also have the smallest possible capacitance and thereforethe largest possible charging energy per electron on the central dot,making the SETs function readily at room or even more elevatedtemperatures. Highly energy efficient circuits composed of SETs can bebuilt.

Consideration to the substrate needs to be given. Two close spacedASiQDs on a single silicon dimer of the Si(100) surface interact morestrongly than do 2 or more ASiQDs generally. The splitting resulting inthat particular case creates states resonant with the bulk siliconvalence and conduction bands. As a result, ASiMs containing two orASiQDs on a single dimer will not have ASiM in the band gap. Theseensembles will leak or be merged with bulk states.

This leakage can be deployed to purposely connect a ASiM with the bulk,so as to electrically connect the ASiM of example.

A single atom with gap states and with the capacity to be in the +1, 0,or −1 electronic charge states can be rendered incapable of holding acharge if coupled to another ASiQD on the same dimer on the Si(100)surface. This can be used to eliminate charge centres and pinningcentres.

On the Si(111) surface, ASiQDs can never be closer than 3.84 Angstromsand as a result cannot achieve large enough splitting energies to createnew electronic states resonant with the valence and conduction bands.

An inventive AsiQD has the attributes of: multiple dangling bonds (DB)on the otherwise H-terminated Si(100) surface, or the H—Si(111) surfaceor other H-terminated silicon surfaces can form quantum dots; a singleDB is a quantum dot that can have three ionization states, it can +1, 0or −1 charged, corresponding respectively to 0, 1, or 2 electrons in theDB state; and all the charge states are in the silicon bulk band gap. Itis appreciated that while the present invention has been detailed withrespect to H terminated surfaces silicon, the analogous inventivedevices are formed above a surface of germanium and carbon. Othersubstrate materials suitable for the similar generation of such danglingbond states illustratively include semiconductor domains havingincomplete surface passivation, specific forms of which includeprotonated surface, locally doped and nanocrystalline domains ofsemiconductors illustratively including silicon, a variety of extrinsicand intrinsic monoatomic, binary and ternary semiconductorsillustratively including silicon, gallium arsenide, gallium phosphide,indium phosphide, germanium, indium arsenide, indium antimonide, galliumaluminum arsenide, cadmium sulfide, zinc sulfide, aluminum indiumphosphide, aluminum gallium arsenide, aluminum indium arsenide, aluminumgallium antimonide, gallium indium phosphide, lead tin telluride, coppergallium selenide, zinc germanium arsenide, and copper iron sulfide, andadvantageous crystallographic orientations of these.

The coupling of DB states occurs by placing multiple DBs together inclose proximity form a larger quantum dot. The multiple silicon atomquantum dot, MSiAQD also has its states in the silicon band gap.

The states being in the gap is crucially important and unique. It allowsfor decoupling of bulk and ASiQD and MSiAQD electronic states. That inturn means electrons in such surface states are effectively electricallyisolated from the bulk. And that isolation in turn means that MSiAQDentities do not require an electrically insulating layer betweenthemselves and the bulk.

In making atom scale circuitry on a silicon substrate, it becomesnecessary and desirable to provide ultrafine, even atom scale wiring tothe active entities of the circuitry. The need for an insulator betweensuch a wire and the silicon substrate enormously complicates, enlarges,and brings spatial and compositional uncertainty to the wires and theirexact relation to the address active entities. As the present inventioneliminates the need for an insulating layer, and the ability to makewires with reproducibly precisely, atomically defined character greatlyenables and advances the act of making atomic level circuitry.Specifically, having known and unvarying relationships betweenelectrical leads and the entities they address leads to near zeroinhomogeneity in circuit properties.

Thus the present invention and these techniques are highly desirable inmemory elements, classical circuitry of diverse type, and to a broadrange of coherent quantum circuitry also.

The dots of the present invention are unique in that current does notflow through the devices.

Atomic Level Device Elements

A charge state transition is seen by recording the AFM signal whilesweeping the bias between sample and AFM tip. This technique, known asKelvin probe force microscopy, KPFM, has been widely applied to studythe contact potential difference between probe and sample, and morerecently, to detect discrete charge state transitions on single Goldatoms.

STM images clearly reveal the atomic structure of silicon dangling bondensembles on H-terminated silicon. AFM images of the same area,collected such that the images are dominated by electrostatic forces,show the positions of the charges and therefore the logical state of thegate. These images are taken at a somewhat larger tip-sample separationdistance than is used for atomically resolved imaging. Electrostaticforces have a longer tail than other forces that contribute to AFMimaging allowing us to record images that are to a good approximationmaps of localized charge.

Tunnel coupled pair of DBs, collectively, have a charge of −1. As thetunneling interaction among DBs falls off exponentially, the somewhatfurther removed perturbing DB is not significantly tunnel coupled to thepair and acts instead as a fixed electron charge. Also, the perturbingDB is not Coulombically destabilized enough to lose its negative charge.Correspondingly, the KPFM transition energies for the perturbing DB andfor the DB furthest from that atom, traces xx1 and xx2 in FIG. 9, aresimilar. The KPFM trace for the middle DB shows a distinctly shiftedcharge transition energy. This shift is due to the repulsive effect ofthe perturbing DB. Accordingly, a relatively positive voltage betweenprobe and sample must be applied to record the negative to neutralcharge state transition of this DB.

Expressed otherwise, the middle DB is seen at zero probe bias, but underthe influence of the negative perturbing DB, is already in the neutralstate. It is evident that the tunnel coupled DB s form a double wellpotential that can be polarized by an electric perturbation. In thisexample, the double well is tilted to the “left”, causing the sharedelectron to tend to localize there.

A fixed charge, or a variable bias electrode, can localize charge to oneside of a double well potential formed of two tunnel coupled DBs.Likewise, in more complex potential energy surfaces due to largerensembles of atomic silicon quantum dots, an applied potential spatiallyshifts electrons. This allows information to be encoded in spatialcharge distributions and for information to be transferred without theuse of a conventional current, with minimal energy consumption peroperation, and with no quiescent power consumption.

FIGS. 8A-8F show multiple DB pairs aligned end to end. As before, asingle perturbing charge is applied at one end (right side) to induceall pairs to align in one of the two available polarized states, FIGS.8A and 8B. In FIGS. 8E and 8F the same line of pairs is polarized fromthe other side. And correspondingly all the pairs polarise to the right.The initial polarising DB in FIGS. 8A and 8B was controllably cappedwith a single H atom, thereby entirely eliminating the gap state thatautomatically sequestered one electron there, and that served as aninput per FIGS. 8C and 8D To demonstrate the two-state line could bepolarised in the opposite sense, a new DB was created at the left sideas shown in FIGS. 8E and 8F.

No reset operation of the line is needed. The two state line isinstantly ready to function again. While not excluded from certainenvisaged applications, in the present embodiment, the scanned probeinstrument is not a component of the device, it is only an observingtool.

The number of atoms per cell may be varied. Additional variants includedifferent intra and inter cell spacing and as well, through Fermi leveladjustment different occupation levels allow for a great many avenuesfor tuning of properties. For the case shown here, it has been estimatedthat the tunnel rate (among two DBs in a pair, there is no significanttunneling between pairs) is approximately 10 fs. It can be seen that theimposed polarisation state is spread along the line, very roughly, at atime that is the product of the tunnel time and the number of cells.This propagation mode takes the place of an ordinary RC time constant,and, readily allows data transmission rates at THz clock rates.

The energy required to switch a cell is approximately the electrostaticenergy required to place an input charge near a single electron occupied2 Db cell; approximately 0.3 eV.

FIGS. 9A-9O shows a binary logical OR gate. The two top most branchesare electrostatic inputs and the lower branch is an electrostaticoutput. All the states of the truth table, shown in FIG. 9C, areexhibited in FIGS. 9A-9D. At the terminus of the output branch is asingle DB that serves as a “spring”. Using highly n-type doped silicon,negative charges can be placed in the current structures but notpositive charges. As a result, the device can electrostatically “push”but not “pull” on the charges controlled. In order to establish oppositepolarisation states of DB pairs as the two binary states, a weakperturber is placed at the terminus of output branches. In the absenceof a negative charge at the input, the line is polarised toward theinput, creating what is labeled a binary state “0”. When a negativeinput is in place, the two state line flips to a state “1”. As the gateis naturally a negative charge repulsive character at the inputs, thespring function required for proper function of a connected output of aprevious gate is assured.

Just as the binary wires require electrostatic inputs and provideelectrostatic outputs, the gates all receive and output electrostaticstates. In various embodiments, the binary wires can be combined withthe binary logic gates. The binary wires convey binary inputs to thegates and convey binary outputs from the gates to subsequent gates or toother receptors of the binary information so computed. The function ofthe gates utilizes combined quantum mechanical and electrostaticphysical interactions.

According to embodiments of the present invention, two or more ASQDs, insuitably close proximity, from 0.14 nm to several 10s of nm, enter intoquantum mechanical associations that allow electrons to tunnel among thecoupled ASiQDs. Electrostatic effects derive from the positive charge atthe nuclei of the ASiQDs and from the electrons bound to or near to theASiQDs. The electrostatic positions of electrons confined to double, ormultiple, well potentials within the gate structure embodies the binaryinformation. Information encoded in the form of electrostatic magnitude,and spatial arrangement, provides inputs to the gates. Upon receivinginputs, the electrostatic interactions within the gate spontaneouslyleads to spatial charge arrangements that provide a logical outputconsistent with the truth table for the particular gate. The timerequired for an output signal to exist after the arrival of inputsignals is a small multiple of the average tunneling time of electronsbetween ASiQDs. For the OR gate shown in FIG. 9, that time is <10⁻¹³.Alternately, expressed as a rate, that is 10 THz, which is 10,000 GHz.

Static electrostatic inputs in the form of singly charged atoms areshown here to demonstrate function of the wires and gates. Analog wireswhich can be biased at any voltage within a range of several 10s ofvolts about the Fermi level and with a resolution of nanovolts or finercan also serve as inputs to the wires and gates.

The bit energy, which is the energy required to change from one binarystate to the other is determined by the strength of quantum mechanicalcoupling among the ASiQDs and is equal to 0.3 electron Volts formaximally coupled ASQDs. More widely spaced ASiQDs can be deployed toachieve smaller coupling energies. This bit energy is larger thankBoltzmann T ensuring that the integrity of information embodied in thismaterial system, for the duration required, is maintained.

According to various embodiments, the gates and the binary wires can beclocked, that is, the rate of passage of information through a logicaloperation can be regulated by a time varying control signal. In thisAsiQD-based circuitry the clock signal provides gain. Gain is requiredto ensure signals are not degraded as sequential operations areperformed. An output is obtained spontaneously upon presentation ofinputs. Latch circuitry in coordination with the clock signal allows theoutput of one sub-circuit element to be retained so as to serve as theinput of a subsequent circuit stage. In some inventive embodiments,inventive dots can be arranged to create fanout—that is, one input to afanout device is copied to provide 2 or more outputs. This allows foroutputs at any stage to be sg=hared with any number of following circuitelements.

The present invention provides very low power consuming circuitry.Because no transistors are employed in this circuitry and because nocurrent is required to charge gates or other elements and furthermorebecause no current is sent to ground, extremely little power is requiredto actuate this circuitry. A fixed number of electrons stay within eachcircuit element. Electrons are merely spatially rearranged to representinformation and to cause computation to occur. Latched inputs enforceinformation flow in the direction from inputs to gate outputs.Subsequent latching of outputs causes passage of information to the nextcircuit stage. According to various embodiments, asynchronous as well assynchronous and periodic clocking and latching can be employed.

The present invention provides many structural options for gates. Themagnitude of spacing among ASiQDs and the angular direction affectscoupling strength, type of interaction.

According to some embodiments, the present invention provides anelectrostatic bias that compensates for our all-negative quantum dots.Because all points are zero charged or negative, charges can be pushedpush but not pulled. Accordingly, placing a charge at a far end ofcircuit elements so allows pushing a charge so it naturally comes backto equilibrium under force of the bias.

The present invention also provides clocking, including both theregulation of information passage and maintenance of signal strength orgain, is achieved by local Fermi level adjustment. In variousembodiments, an electrode near to a logical circuit block, consisting ofmultiple inputs, outputs and gates, raises or lowers the potential inthe vicinity of the circuit block so as to change the electronoccupation of ASiQDs. Either change blocks the passage of informationalong binary wires and through logic gates. By enforcing desired inputvalues at the edge of the sub circuit while the Fermi level adjustingelectrode is returned to its regular value corresponding to electronoccupation that gives desired logic functions, the sub circuit reaches aground state free of kinks and the correct output value is established.The settling time of the output is of the order 10⁻¹³ seconds.

The present invention also provides positive and negative charge basedcircuitry. At different doping levels or at different electrostaticallyset Fermi levels, the circuits are made from zero charge rather thannegative charge quantum dots. This provides for binary but also analogand quantum circuitry. Elements as used here for classical computingtogether with other ensembles can be made from the inventive quantumcircuitry elements.

According to embodiments of the present invention the quantum dots areencapsulated. That is, the inventive quantum dots are in permanentvacuum encapsulation. DBs not immediately adjacent to another DB aregenerally unreactive toward common gaseous molecules including N2, O2and many hydrocarbons.

According to embodiment of the present invention, a line of tunnelcoupled ASiQDs with multiple perpendicular analog or binary wires formsa shift register. The register can be of arbitrary length. Similarly, aring Oscillator is provided. A cyclic sequence of inverters forms thering oscillator. A flash analog to digital converter and a digital toanalog converter can also be made. Resonant structures capable ofinteracting with external or locally provided electromagnetic fields(for signal input/output or signal processing/transduction) aresimilarly enabled.

Using the present invention, many forms of A/D can be made. Ofparticular interest is a flash A/D drawing low power. The presentinvention also provides for a frequency divider. That is, a multi stagebinary frequency divider for radio telephony front end with inputfrequencies up to 10 THz.

The present invention is further detailed with respect to the followingnon-limited experimental examples.

Experiment Set-Up

DBs are created controllably with the probe of a scanned probemicroscope. A voltage and or current larger than is used for imaging isapplied briefly to the H atom to be removed. Current rises when an Hatom is removed. Upon checking for that change and finding H removal,the electrical conditioned applied to break the specific targeted Si—Hbond is ceased. Re-imaging reveals the newly created DB. Patterns arecreated by placing the tip over desired positions and removing multipleH atoms thereby creating multiple DBs.

A lock-in amplifier collected the dI/dV signal at each point. Thus, thelocal density of states, LDOS, of the DB chain as a function of voltage(usually from −0.4V to −1.8V) have been mapped out. The experimentaltechnique is not sensitive to z-drift (tip sample separation) as the tipheight is reset each time a line or map is completed. The z-drift isestimated in the time taken to move along a line or scan over a map, amaximum of 3 minutes, is negligible.

Experiments were conducted in an Omicron Low Temperature STM at 4.5Kunder ultra-high vacuum (UHV). A lock-in amplifier was used to measuredI/dV signal (modulation frequency of 760-820 Hz and amplitude of 30mV).

Arsenic doped (0.002-0.003 mOhm/cm) Si (100) samples were direct currentheated to 1050 C for a short time for oxide desorption, and hydrogenterminated at 330 C for ˜20 s under hydrogen exposure, forming theH—Si(100) 2×1 surface. It is known that flashing to 1050° C. does notsignificantly remove dopants in the near-surface regime and so a uniformdopant profile persists all the way to the surface.

Polycrystalline electrochemically etched tungsten tips were heated to˜800 C for about two minutes under UHV condition for cleaning and oxidedesorption. Their quality was checked by field ion microscope (FIM), andnitrogen etched to obtain single atom tips. Small tip modifications weremade during STM measurements by slightly contacting the tip with a patchof bare Si while applying a voltage of −2 to −3V.

An algorithm has been developed to facilitate atomically precise DBpatterning. The tip was placed over the desired location and a train ofvoltage pulses was applied to desorb hydrogen. Successful hydrogendesorption was checked by comparing the current set-point before andafter applying each pulse. The voltage magnitude for each pulse wasincreased in small increments until a desorption was detected. In thisway, two to seven long DB chains were patterned along and on the sameside of a dimer row in the closest spaced arrangement allowed by thelattice (0.35 nm).

EXAMPLE 1

FIG. 1 shows various characterisations of a linear 3 DB MSiAQD formedalong one side of a dimer row on the Si(100) H terminated surface.

The large dI/dV vs position graphic conveys much information about theenergy and spatial distribution of local state density. In other words,it shows where electrons are localized, and not, at each energy probed.

At most energies, strikingly, little state density is observed at thecentral atom position. This is a great and clear departure from thesingle ASiQD result. It clearly shows the emergent molecule likespectroscopy of the ensemble resulting from quantum mechanical overlapof atomic like orbitals.

Close space DBs form substantial electron sharing bonds. The newlyemergent electronic structure is observed in multiple modes of imagingwith a scanning tunneling microscope (STM). Spatially point specificdI/dV spectra show pronounced changes indicating new electronicstructure. Whole 2D images of dI/dV, taken at a specific V show localdensity of states variations at that energy across the area of the newmultiple silicon atom quantum dot. This is a new artificial moleculewith tailored density of states to allow an externally applied(vertical) electrostatic field (i.e. Fermi-level tuneable) to alter thelateral 2D charge multipole distribution. As a result, an artificial 2Dmolecule according to the present invention operates akin to a fieldtransducer to allow the external vertical field (by varying total chargeand/or spatial occupation of charge) to have unprecedented Angstromscale control of lateral field shape/sharpness/direction on the surface.

dI/dV spectra over a range of voltages, taken along a line from one endof a molecule to the other, reveal a whole spectral map of themolecule's density of states.

Clearly emergent structures in LDOS are noted as DBs are brought closetogether (and wavefunctions overlap). This is proof of mixing of DBwavefunctions and the formation of collective states or what can equallybe called molecular states.

Further to the 3DB Chain in FIG. 1. FIG. 1(a, b) shows STM constantcurrent images collected at −1.8V and 1.4V respectively. The setpointcurrent was 50 pA. In Filled states, the 3DB chain appears as two brightspots. In empty states, the 3DB Chain appears as one bright spot spreadover the length of the chain. FIG. 1(c-e) show constant height dI/dVmaps taken of the 3DB chain at three different bias voltages: −0.9V,−1.05V, and −1.7V. Note that the color scale for the three dI/dV maps isdifferent for each map. FIG. 1(f) shows a plot of dI/dV linescans alongthe axis of the 3DB chain, shown in a dotted line in (a), from −0.4V to−1.9V with 10 mV resolution. For (c-f), the tip height was set at −1.8V20 pA over an H—Si dimer near the chain with 60 pm tip retraction afterthe feedback loop was turned off. We observe a change of the patterns indI/dV maps and linescans as the voltage is increased. We identify threeregions where the dI/dV patterns take on different character for this3DB Chain: From −0.6V to −1.0V they take on the appearance of two brightspots. From −1.0V to −1.2V they take on the appearance of two dark spotsin the same spatial location. We observe negative differentialresistance within the spots, with two bright rings that surround thespots. Finally, From −1.2V to −1.9V we observe two bright spots onceagain.

FIG. 2 shows similar results for a variety of other chain lengths. Inall cases there are no Si—H entities in between the DBs. Rather, the DBsare as close together as the silicon lattice allows, 3.84 Angstroms.

When H atoms intervene between DBs, as is the case in all but oneprevious published example, the strong mixing and bind of atomic statesdoes not occur and the qualities describe here are not observed. Whenintervening H atoms exist between DBs the images of such widely spacedensembles reveal only a simple sum of the qualities of the constituentparts—not—as seen here—newly emergent properties that ire non-linearlyrelated to the properties of the parts.

In FIG. 2 it is seen that diverse electronic properties are observed asa function of number of constituent atoms, as well as of functions ofenergy and position.

In the dI/dV maps of DB chains of length 4, 5, 6, and 7 in FIG. 2 eachcolumn corresponds to one DB Chain length. The first image of eachcolumn is an STM constant current image of that chain, imaged at −1.8Vwith a setpoint current of 50 pA. The remaining images are dI/dV maps ofthat chain taken at a tip height of −1.8V, 20 pA with a tip retractionof 60 pm over a H—Si dimer. All chains the patterns in dI/dV maps arenoted to change as a function of sample bias. The bright spots often donot correspond to the locations of the DBs. Thus the patterns must beemergent from an interaction between the DBs that make up the chain.Most STM images and dI/dV maps are symmetric about the center of the DBchain. The 5 and 6DB chains in (b,c) were made by extending the 4DBchain in (a). Knowing this, we note that similar features appear atsimilar voltages for the 4,5, and 6DB chains shown: At a sample biasbetween −1.7V to −1.75V, the dI/dV maps show the same number of brightspots as the number of DBs in the chain. For the 5 and 6DB chain at asample bias of −1.8V, the dI/dV maps appear to show spots with negativedifferential resistance.

FIG. 3 is different qualitatively from above results, not only in thatit is a seven atom chain, but because the electronic perturbation ofthat chain is also demonstrated.

FIG. 3 shows the perturbation effect of a localized charge on a 7DBchain. The STM image and the dI/dV linescan of the unperturbed chain(FIG. 3(a)) exhibit emergent patterns. The patterns are symmetric aboutthe center of the DB chain. A significant dI/dV signal begins at asample bias of about −0.6V.

In FIG. 3(b), we see the same 7DB chain perturbed by a single DB on thesame side of the dimer row with one intervening H—Si dimer. The STMimage shows higher topography on the end of the chain furthest from theDB and the overall pattern is changed compared to the unperturbed 7DBchain. The dI/dV linescans show higher state density on the end of thechain farthest from the single DB. They show patterns very differentfrom that of the unperturbed 7DB chain. Although a faint dI/dV signal isseen from −0.6V to −0.9V, it is substantially less than the magnitude ofthe signal seen at the same voltages on the unperturbed 7DB chain.

These observations show that by placing a DB, or a localized charge,next to the 7DB chain, we electrostatically influence the chain andcause its electron state density to shift away from the perturbinglocalized charge. The localized charge also increases the energy of allelectrons on the chain, causing a great reduction of state density atlower voltages, −0.6V to −0.9V, compared with the unperturbed 7DB chain.

A single DB naturally attains a negative charge on a highly dopedsubstrate as is used here. It is that localised charge that iselectrostatically altering the properties of the adjacent MSiAQD.

Surprisingly, creating another DB immediately adjacent to the firstperturbing DB, specifically on the same underlying si dimer, reduces henegative charge localised in the vicinity. This reduction in chargelocalisation occurs because the strongly interacting nature of 2 DBs onone dimer causes a large energetic splitting. So much so that the newsymmetric and antisymmetric states created—often referred to as pi andpi star states, are resonant respectively with the bulk silicon valenceand conduction bend edges. As a result the electrons do not localise butare rather disbursed in those bands.

Upon replacing the single perturbing DB with 2 DBs of a bare Si dimer itis evident that the STM images and dI/dV linescans of the 7DB chain havereturned to the unperturbed state.

In addition to showing the reversibility of the electronic perturbationeffect on the MSiAQD, this effect demonstrates that utility of a cleandimer as a way to connect gap states such as those we create with ASiQDsand ensembles thereof to bulk states. One wire of multiple wiresrequired to connect and operate a atom scale structure could be providedby the bulk, thereby greatly reducing the number of wires required, andreducing complexity, and increasing circuit density and simplicity.

An end to end arrangement of paired DB s can also form an effectivewire. In FIG. 4 shows 2 DBs, separated by one Si—H unit on the H—Si(100)surface. This pair is a charge qubit. The lower part of the figure showsthat same pair of DBs being perturbed by a third, negatively charged DB.Polarization of the pair is evident. As dark shading in these chargesensing atomic force microscopy images corresponds to negative charge,we see that the DB closest to the perturber is rendered relatively lessnegative.

In FIG. 5, an elaboration of FIG. 4—an extremely important elaborationis shown—of the effect show above. Here, two qubits are formed. When thesame perturbation as per FIG. 4 was applied—the same result was achievedin the nearest qubit. Remarkably, in addition, it is noted that thequbit directly biased by the perturber has in turn biased the secondqubit. Note the most perturbed DBs are still present but rendered herealmost invisible. These electronic changes are entirely reversible.

These results show a degree of single atom and single electron chargecontrol that have never before been demonstrated. The ability to harnessand deploy this to achieve controlled interaction within a cluster ofentities is clearly demonstrated also. That the control is manifest onsilicon, and using the entities we desire is of diverse utility.

EXAMPLE 2

This experiment shows the ability to form more complex and advanced atomscale electronic structures from multiple ASiQDs according to furtherembodiments of the present invention. Such structures have utility inbinary computation or atomic binary logic

FIG. 6A shows a constant current STM image of an ASiQD created bytip-induced desorption of a single hydrogen atom from the H—Si(100)surface. At relatively high voltages (e.g. −1.7 V), the negativelycharged ASiQD appears in filled states images as a bright protrusionsurrounded by a characteristic small dark halo (17). In thecorresponding frequency shift map at 0 V (FIG. 6D)), hydrogen atomsdecorating underneath silicon atoms appear as bright protrusionsarranged in the 2×1 surface reconstruction. The ASiQD shows up as a darkfeature indicating a much higher tip-sample attractive interaction (19).

FIG. 6C shows I(V) spectroscopy curves taken above the ASiQD and H—Sisurface, with both the surface and ASiQD showing a zero current bandgapfrom around −0.8 to +0.2 V. FIG. 6D shows the Δf (V) spectra, i.e. KPFMspectroscopy, measured above the ASiQD with a bias sweep range of −0.6to 0 V, a range in the bandgap of the material where no STM informationwould be available. Interestingly, a sharp step is seen at around −250mV. Prior work examining charged species (6, 21), electron transferbetween molecules (7), and charge state changes in quantum dots (25) inNC-AFM experiments has shown this type of step feature to correspond toa dynamic single-electron charge state change. Therefore, based onprevious works, the step seen in FIG. 6D can be assigned to the chargestate transition of the ASiQD from negative (doubly occupied) to neutral(singly occupied) charge state, respectively right and left of the stepin the Δf (V) curve around −250 mV.

When 2 ASiQDs are closely spaced, within about 1 nm or less, Coulombicrepulsion causes one of the pair's extra electrons to delocalize in theconduction band (14, 22). That loss of an electron creates an unoccupiedstate in the pair of ASiQDs. That, and the low (0.5 eV) and narrowbarrier between the atoms makes tunneling between the paired ASiQDspossible. FIGS. 7A-7I explores polarization of one of these tunnelcoupled pairs of ASiQDs.

FIGS. 7A and 7B show an STM image of an isolated ASiQD and thecorresponding frequency shift map. The Δf (V) spectra (FIG. 7C) shows acharge transition step at −0.2 V, Additional ASiQDs are added, but withcare to ensure no tip changes with the addition of ASiQDs, and withidentical parameters for AFM and KPFM. In FIG. 7D a second ASiQD iscreated that is tunnel coupled to the first ASiQD from FIG. 7B. The AFMimage in FIG. 7E shows 1 intervening hydrogen atom between the pair,with a similar contrast observed above both ASiQDs. The KPFM measurementin FIG. 7H corroborates this, showing nearly identical AFM curves takenover the 2 ASiQDs, with the charge transition step shifted to a lessnegative value occurring now around −0.25 V. The tunnel coupled pair ofASiQDs, collectively, have a charge of −1, which accounts for thishorizontal shift.

A 3rd ASiQD is added in FIG. 7G, with the AFM image in FIG. 7F showing a4 H atom separation. This perturbing ASiQD is not significantly tunnelcoupled to the pair as the tunneling interaction falls offexponentially, nor Coulombically destabilized enough to lose itsnegative charge. A stark contrast is noticed in tunnel coupled pair. Themiddle ASiQD is significantly lighter than the farthest ASiQD. Delvingdeeper and looking at the KPFM curves for this “2+1” experiment in FIG.7I (a color coded inset is in the bottom left of FIG. 7I), it is noticedthat the KPFM transition energies for the perturbing ASiQD (black) andfor the ASiQD furthest left(blue) are markedly more negative than themiddle ASiQD (red). The KPFM trace for the middle ASiQD shows adistinctly shifted charge transition energy to +200 mV. This shift isdue to the repulsive effect of the perturbing ASiQD. A less negativevoltage between probe and sample must be applied to record the negativeto neutral charge state transition of this ASiQD. Expressed otherwise,it can be seen that the middle ASiQD at zero probe bias, but under theinfluence of the negative perturbing ASiQD, is already in the neutralstate. It is evident that the tunnel coupled ASiQDs form a double wellpotential that can be polarized by an electric perturbation. In thisexample, the double well is tilted to the left causing the sharedelectron to tend to localize there.

Accordingly, the present invention proves a fixed charge, or a variablebias electrode, that can localize charge to one side of a double wellpotential formed of two tunnel coupled ASiQDs. This allows informationto be encoded in spatial charge distributions and for information to betransferred without the use of a conventional current, with minimalenergy consumption per operation, and with no quiescent powerconsumption.

Expanding on this principal, FIGS. 8A-8F and 9A-9O show multiple DBpairs aligned end to end, creating atomic binary wires and atomic binarygates. STM images shown in these figures reveal the position of atoms.On the other hand, AFM images in certain height regimes show theposition of charges in the structure, and therefore reveal the logicalstate of the atomic wires or gates. Notably, the AFM images were takenat larger tip-sample separations where electrostatic forces are dominantin order to visualize the transmission of information easier. Therefore,they do not resolve the surface structures as seen in Reference (26) andFIGS. 6 and 7.

FIGS. 8A-8F show a STM filled states image of a fabricated 17, 18 and 19ASiQD atomic binary wires. Colored circles underneath each structure areadded for clarity to show the position of negative (blue), neutral(light green) and perturber (red) ASiQDs. FIGS. 8A-8F show an atomicbinary wire consisting of 8 coupled pairs and a lone un-coupled DBacting as a perturber on the far right. DBs in a pair have a single Hatom separation, and pairs are 4 H atoms from each other. Below the STMimage in FIG. 8A is a constant height AFM image of the structure in FIG.8B. As before, the far right single perturbing charge breaks thesymmetry and induces all pairs to align in one of the two availablepolarized states (tipping left). FIG. 8C shows a STM image of there-symmetrization of the wire, with the far right DB now turned into acoupled pair. The wire reacts by dividing down the middle in thefrequency shift map of FIG. 8D with half falling left, and half fallingright. The symmetry plane is marked with a dashed white vertical line inthe AFM image. Finally, in FIGS. 8E and 8F, the same line of pairs ispolarized from the opposite side with a 19th DB added on the left. Thewire responds by assuming the other remaining polarization state(tipping right), reversing what was shown in FIG. 8A.

Accordingly, the present invention demonstrates a reversible informationtransfer expending only the entropic energy associated with rearrangingelectrons in coupled wells, while also showing no reset of the line isneeded. The two state line is instantly ready to function again. Thescanned probe instrument is not a component of the device, it is only anobserver.

FIGS. 9A-9O show a binary logical OR gate according to the presentinvention. The two topmost branches are inputs, and the lower branch anoutput. FIG. 9A shows the “central” structure comprising the gate: 3tunnel coupled pairs arranged at sharp angles and meeting in the center.Isolated from any electrostatic influence, the 2D assembly experienceselectrostatic repulsion among the pairs, with electrons localizing tothe outside of the branches as indicated by the contrast in the AFMfrequency shift map in FIG. 9B.

In order to establish an opposite polarization state of the outputASiQD, an adaption is made and a weak perturber at the terminus of thelower output branch is used as demonstrated in FIG. 9D. This perturberacts as a “weak spring”, polarizing the bottommost ASiQD from thecentral structure to be neutral, which is defined as the 0 state. Thisis shown experimentally in FIG. 9E and graphically in FIG. 9F. The firstrow of the truth table is established with two 0 inputs giving a 0output.

When a negative input is in place at either the top left FIG. 9G, topright FIG. 9J, or both FIG. 9M input branches, the weak spring isovercome at the output with electrons in the structure rearrangingaccordingly and flipping the 0 state of the output to a 1 state as seenin the AFM maps FIG. 9H, FIG. 9K, and FIG. 9N respectively. Correlatingthis to the gate output models FIGS. 9I, 9L, and 9O, this fulfills therest of the truth table. To complete the truth table, FIG. 9J isachieved by passivating the ASiQD input on the left in FIG. 9G usingmechanical passivation, and creating the new input on the right.

Spectra of local force as a function of applied voltage reveal chargestate transitions of single dangling bonds and of ensembles. Singleelectron induced switching of a double dot entity, and of a longsequence of double dots, from Left to Right or binary 0 and 1 states hasbeen shown. A binary OR gate including all states of its truth tablehave been shown. It is also contemplated that extension of signals wellbeyond the gate output as well as NOT and AND functions among others.

Because the gates and the binary wires between gates require only singleelectron-level electrostatic actuation and because no conventionalcurrent is required, power consumption is extremely low. As the tunnelrate among coupled atomic quantum dots is of the order of femtoseconds(NJP paper on qubits 2010) signal transmission and gating action will befast. THz operation rates are anticipated. The approach described heremay enable a beyond Moore technology combining as it does enormous speedwith ultra low power consumption while eliminating transistors.

Experiment 3—Process of Creating an ASiQD

Inventive ASiQDs are formed using an inventive process in which verticalmanipulation of a single H atom using the tip of an AFM sensor and itsapplication in characterizing and engineering silicon DB-basedstructures of relevance to nanoelectronic devices. Following a localizedtip induced excitation on the Si—H surface, a single hydrogen atom isdesorbed and may be either deposited on the surface with stable imagingin STM and AFM, or transferred to the tip apex. The single H atomfunctionalized tip is identified through a unique signature in frequencyshift vs. displacement curves (i.e. Δf(z)) and a characteristicenhancement of STM images in filled and empty states. By bringing theH-functionalized tip apex very close to a DB in the absence of bias andcurrent, a covalent bond between the single hydrogen and silicon atomsis formed. Subsequent changes in the STM images and Δf(z) curves confirmthat this mechanically induced reaction results in the passivation ofthe DB with the hydrogen from the tip apex.

CO functionalized tips are effective for characterization of adsorbedmolecules on metal surfaces.(24, 28) The present inventive processprovides embodiments of a process for preparing and identifyingaccessible and effective H functionalized tips, which allowcharacterization and also induce changes in DB-based structures on theH—Si(100) surface through selective mechanically induced hydrogenpassivation, or “capping.” Deuterium capped tips can be made similarly.Deuterium capping of ASiQDs can be achieved with such tips.

In the Si(100)-2×1 reconstruction, silicon atoms at the surface areorganized in dimers. When the surface is passivated with hydrogen in themonohydride reconstruction, each silicon atom at the surface iscovalently bonded with a single hydrogen atom as represented in FIG.10A. FIG. 10B shows a typical defect-free empty states STM imageacquired using a non-functionalized tip (see methods and ref (29) fordetails on in situ tip preparation).

FIG. 10C shows a 3D ball and stick model of a silicon dangling bond(represented in green) on the H—Si(100) surface. To create a single DB,the STM tip is positioned on top of a hydrogen atom (red dot in FIG.10B), then the feedback loop is switched off, and a voltage pulse ofabout 2.3 V is applied for a few milliseconds. As illustrated in FIG.10C, this results in the selective desorption of the hydrogen atom underthe tip apex which is often transferred to the tip. FIG. 10D shows atypical STM image of the created single DB. In accordance with earlierstudies in the literature, the DB in empty states appears as a brightprotrusion surrounded by a characteristic dark halo. (11, 14).

According to embodiments of the inventive process, the desorbed H atomis transferred to the tip apex roughly 50% of the times, i.e. forming aH-functionalized tip. In 30% of cases, the desorbed H atom is found onthe H—Si surface close to the just created DB, as shown in FIG. 11A. Inthe remaining 20% of cases, the tip apex does not change and a hydrogenatom could not be seen in the vicinity of the newly created DB,suggesting it was possibly adsorbed on the tip away from the apex atom,deposited on the surface farther from the DB, or ejected to the vacuum.

FIG. 11A shows an example of a single hydrogen atom found to bedeposited on the H—Si surface immediately after tip induced creation ofa DB. Such an object is confirmed to be a single hydrogen atom bydragging it with an elevated positive bias to passivate the creatednearby DB (FIGS. 15A-15C). Interestingly, the hydrogen atom appears inempty states STM images as a slightly bright protrusion surrounded by adark halo as shown in FIG. 11B. This suggests a charging effect thatinduces a localized band bending similar to a single DB. (14, 16) In thecorresponding frequency shift map (FIG. 11C), the physisorbed hydrogenatom appears to induce a lattice distortion of two adjacent dimer pairs.When imaged at relatively high positive voltage (+1.6V in the example ofFIG. 2-f), the hydrogen atom is picked up by the tip apex as evidencedfrom the change in STM contrast midway through the scan.

In the examples of FIGS. 10A-D and 11A-D, the enhanced STM contrastafter creating a DB is a first strong indication of tipfunctionalization with the desorbed single H atom. The contrast changesfrom resolving dimers (FIG. 10B) to resolving single atoms (FIG. 10D),respectively, before and after the hydrogen desorption from the surface.This is similar to what is well known for the CO molecule, where once itis picked up by the tip apex following a voltage pulse it enhances theSTM and AFM contrast.(24, 30, 31) Identification of different tipdynamics is accomplished through studying force curves.(25, 29, 32)Mechanically induced covalent bonding of single hydrogen and siliconatoms. FIG. 12A shows a filled states STM image of the H—Si surface witha silicon DB created using the inventive process. Similar to the case ofempty states, an enhanced STM contrast is noticeable. In fact, typicalfilled states STM images of the H—Si surface usually show only dimerrows,(14) but in FIG. 12A the dimers of dimer rows are clearly resolved.

Scanning the single DB of FIG. 12A in AFM scanning mode, FIG. 12B showsa frequency shift vs. displacement curve recorded using a hydrogenfunctionalized tip on top of a hydrogen atom on the surface. The minimaat around −3 Å is always seen when a functionalized tip is preparedfollowing the procedure previously described. Such features are ascribedto the relaxation of the functionalizing atom at the tip apex. (7, 28,33).

When recorded on a DB using the same functionalized tip, Δf(z) curvesexhibit a hysteresis between the forward and backward sweep when the tipis brought very close to the DB as shown in FIGS. 12C and 12D, whichindicates a change in the AFM junction.(10, 33, 34) When acquiring asubsequent STM image, it is noticed that the DB is capped with ahydrogen atom. The defect indicated by the yellow arrow is used as amarker showing that FIG. 12E is exactly the same area as 12A.Additionally, Δf(z) curves recorded on top of a hydrogen atom of thesurface as shown in FIG. 12F no longer exhibit the minima characteristicof the hydrogen functionalized tip. This shows that the tip that yieldsthe minima in force curves is indeed functionalized with a singlehydrogen atom.

A tip that produces enhanced STM also systematically produces thecharacteristic force curves with the shallow minima. Therefore, changein the STM contrast, such as presented in FIGS. 10D, 11A, and 12Aindicates successful functionalization of the tip apex with a singlehydrogen atom. This is important for technological applications relatedto altering DB engineered structures through capping, as changes in STMcontrast to detect H-functionalized tips is a much faster indicator thanthe time-consuming acquisition of Δf(z) curves. In fact, regularsystematic, non-tip-damaging, and reliable capping is produced using STMcontrast as an indicator alone.

All Δf(z) curves were recorded at 0 V in the complete absence of tunnelcurrent, and the hydrogen capping of the DB only occurs when the tip isbrought to a close enough interaction distance. Therefore, thesilicon-hydrogen covalent bonding is mechanically induced. Notably,mechanically induced desorption is also observed, but often results intip structure changes or multiple hydrogens desorbed, unlike the gentleand precise tip induced desorption. The initial tip apex structurebefore picking up a hydrogen atom on the tip apex is never exactly thesame. So, the H-tip bond is not necessarily the same in allH-functionalized tips, similarly to the case of CO tips. This results invariation on the tip elevation to induce capping. Other factors such asthe sensor oscillation amplitude or the Δf(z) acquisition parametersalso play a role.

In addition to high resolution AFM imaging, H-functionalized tips can beimplemented in atom-by-atom lithography to create and modify silicon DBbased nanoelectronic elements.

AFM provides an important complementary view to STM works as it allowscharacterizing the chemical reactivity of DBs. Moreover, unlike STM, AFMallows probing the electronic properties of DBs and DB structures in theband-gap with minimized perturbation from the tip, e.g. minimal tipinduced band bending and electron/hole injection.(14, 15)

FIG. 13A shows force curves acquired using a H-functionalized tip abovea surface hydrogen atom (blue curve) and a single silicon DB (redcurve). These force curves were recorded subsequently with Z=0 Åcorresponding to the tip position defined by the STM imaging set points(30 pA and +1.3 V) before switching off the feedback loop. Hence,superposing the 2 curves allows direct comparison of the interactionforce between tip-surface and tip-DB. It is noticed that for relativelylarge tip-sample distances, the two curves are almost identical. Onlyfor small tip elevations (around −3.5 Å in this example) is a differenceseen, with the DB showing a much larger increase in attractiveinteraction with the tip. This indicates that short range forces are themain contributor to the interaction force. (35) This is also consistentwith the DB being a reactive chemical center on the chemically inertH—Si surface where deposited molecules can selectively adsorb.(36, 37)Similar to what was reported previously for the case of gold atomsadsorbed on NaCl over Cu(111),(38, 39) the short range electrostaticforce due to the localized negative charge on the DB (11, 13, 14) ismost likely the main contributor to the large tip-sample interaction onthe DB.

FIGS. 13B and 13C show frequency shift maps acquired at different tipelevations using a H-functionalized tip. At relatively large tip-sampledistances (FIG. 13B), each hydrogen atom decorating a silicon atomclearly appears and follows the dimer structure of the 2×1reconstruction. The DB arising from the desorbed hydrogen atom on thesurface appears as a dark atom-sized protrusion, introducing a muchhigher tip-sample interaction force localized on the DB. Closer to thesurface (FIGS. 16A-16E), an evolution from atomic to bond contrast isseen on the H—Si surface as discussed in detail in reference.(29) InFIG. 13C, as a result of the larger attractive forces, the DB appears asan enlarged feature. The perturbations seen inside are an artifact inthe excitation channel due to the inability of the feedback loop tomaintain a constant oscillation amplitude (FIGS. 17A-17C).

High resolution bond contrast imaging is rendered possible thanks to thepassivation of the tip apex with a hydrogen atom. (24, 29) The later canbe attracted to form a covalent bond with the silicon DB, but only atvery small tip-sample elevations. This shows that the H-functionalizedtip is robust and can be used to image reactive adsorbates or surfacedefects.

Using atom-by-atom lithography with the STM tip, the coupling betweenDBs can be exploited to create functional DB structures such as QCAcircuits, binary wires and logic gates.(11, 12, 17) For large many-atomcircuits this necessitates a precise control of desorption, which isdifficult to achieve and has not been reported for more than a few DBsso far. Hence, a technique to correct or change multi-DB structures ishighly desirable. Additionally, capping DBs allows modulating theengineered quantum states from coupled DBs.(16)

FIG. 14A shows a filled state STM image of two separate pairs of coupledDBs along the same dimer row. Notably, the H-functionalized tip has anenhanced STM contrast characteristic. In FIG. 14B, the right side DB wasselectively capped using the mechanically induced H—Si covalent bondingdescribed in the previous section. FIG. 14B shows the change in the STMcontrast as previously shown in FIGS. 11 and 12. Additionally, the nowsingle DB on the right side of the image appears as a bright protrusionsurrounded with a small dark halo, while the appearance of the two othercoupled DBs shows no change.(11)

A similar experiment is shown in FIG. 14C where three tunnel coupled DBsare imaged using a H-functionalized tip. The central DB is then erased,the tip re-functionalized by picking up another hydrogen atom, and theremaining two DBs re-imaged in FIG. 14D. Using an equivalent hydrogentip for the before and after images highlights that changes inbrightness are the result of coupling alterations, not simply a changeof the terminating atom.

FIG. 14E shows a filled state image of four DBs along the same dimer rowwith each DB separated by a single H atom as illustrated in the 3D modelof FIG. 14F. In the corresponding empty states image (FIG. 14G), a morecomplex structure is seen with four additional bright protrusionsbetween the visible end atoms. The extra protrusions as an excited statemolecular orbital from wave function overlap of multi-DB systems. Weshow here an active modification of these artificial molecular orbitalsthrough the controlled mechanical covalent bonding of a Si atom (DB)with a hydrogen atom on the tip apex causing nodes to disappear. FIGS.14F and 14H respectively show the altered filled and empty statemolecular orbitals from erasing the far right DB in FIG. 14E. The filledstate image shows up as three bright protrusions corresponding to threeDBs, whereas the empty state image has been altered to now only have 2bright protrusions instead of the prior 4. As shown in FIG. 14E to 14H,DB structures are imaged using a non-functionalized tip both before andafter alteration. This further highlights that changes in the couplingbetween DBs visible from the different additional nodes thatappear/disappear is not due to changes in the tip, but rather the resultof erasing a DB with a hydrogen on the tip apex.

Through the examples of FIG. 14A-14H, it is seen how the controlledmechanically induced H and Si covalent bonding allows thenon-destructive editing of a DB structure. This technique could befurther applied to actuation of more complicated DB based patterns andelements as well, with erasure of a DB acting as a type of switch.

Experiment 4—Indications of Chemical Bond Contrast in AFM Images

The chemical bond contrast observed is usually interpreted as either theintramolecular structure of molecules or intermolecular bonds. It hasbeen suggested that this contrast arises from the Pauli repulsive forcethat becomes dominant at small tip-sample distances (1,18).Alternatively, it is based on a classical force field model (9,19), theflexibility of the tip has been claimed to be the dominant effectleading to the chemical bond contrast in AFM images.

The chemical bond contrast when imaging the H-terminated Si(100) surfaceis consistent with the silicon covalent bond structure of the 2×1reconstruction. This non-planar surface exhibits various Si—Si and Si—Hbonds at different orientations with the H atoms near perpendicular tothe surface plane. First, the Si—Si dimer is parallel to the surfaceplane, providing the first non-adsorbed molecule subject to test theAFM's ability to image bonds. The bond is also uncommonly long, ˜2.4 Åcompared with <1.5 Å for the carbonaceous species studied to date,allowing the probe greater access to the space between covalently bondedatoms. Termination of the dimer with H atoms forces the constituentsilicon atoms to retain an sp³-hike character, thereby preventing thedimer from buckling substantially out of the surface plane (24). Anotherunique feature of the dimer as a specimen for AFM study is its purely σbond character. Unlike the π bonds studied to date, the σ bond decaysmore sharply in the direction perpendicular to the surface and thereforemore nearly approximates the ‘stick bond’ we schematically draw betweencovalently bonded atoms. Lastly, the fixed and exactly known proximityof 2 H atoms on two H-terminated dimers aligned end to end (that is twodimers in adjacent dimer rows) provides a wonderful opportunity to testrecent conjectures related to false indications of bonds whenH-containing molecules are closely juxtaposed.

Following an ex situ cleaning with ebeam and field ion microscopy (FIM),a qPlus sensor with a tungsten tip can be prepared in situ with thehydrogen-terminated silicon surface to obtain either a reactive or apassivated tip, both identified from the typical force curves theygenerate. Using a density functional tight-binding (DFTB)-based approachefficiently simulates AFM images at precisions on par with DFT.

Implementing the ex situ tip cleaning procedure using ebeam and FIM,results in scanning tunnelling microscopy (STM) atomic resolution of thesurface right after the approach. However, images often exhibitartifacts, such as a double/multiple tip as seen in FIG. 18A, thatrenders data interpretation inaccurate. Therefore, it is necessary tofurther process the tip by in situ techniques to obtain a single atomtip apex. When studying metal surfaces, this is usually done by applyinglarge voltage pulses and harsh indentation of the tip into the surface,followed by functionalizing the tip using a molecule such as CO¹. Agentle procedure that gives stable tips without ravaging the studiedsurface area is used.

The method starts by bringing the tip in controlled contact with thesilicon surface, which produces a silicon tip apex (26). A bare siliconarea is then created on the H—Si(100) surface by tip-induced hydrogendesorption (27-29). In the example of FIG. 18A, a (5×5)nm² square areais created by scanning at 4V and 150 pA for about 6 min, coating thesilicon tip apex with hydrogen. The tip is then brought close to thebare silicon area before a new STM image is acquired to check possibletip changes. This procedure is repeated until a sharp artifact-free STMimage of the surface is obtained as shown in FIG. 18B. The small darkfeatures indicated by red arrows in FIG. 18B are H-terminated silicondimers created after the above tip preparation and H termination processwas complete. The tip was positioned over a hydrogen-free dimer, thenmoved ˜6 Å closer to the surface. Reimaging revealed the newlyH-terminated dimer. Similarly, prepared H-terminated dimers have beenpreviously described (30). This capping of silicon dimers with H atomswas done to indicate the presence of multiple H atoms on the tip as aresult of the H desorption preparation process.

The passivated character of the tip is further confirmed using forcespectroscopy. Typical force curves of the H—Si surface acquired beforethe hydrogen desorption procedure, as in the example of FIG. 18C,clearly show a very reactive character. On the other hand, force curvesacquired afterwards, as in FIG. 18D, show a passivated character. Thisis reminiscent of the difference observed between reactive metal tipsand CO-passivated tips (23,31). Approaching the H-passivated tip veryclose to the surface can result in changing the tip back to reactive.Therefore, it is possible to switch between reactive and passivatedtips.

FIG. 19A presents a ball and stick model of the H—Si(100)-2×1 surfacestructure where the different σ bonds between silicon atoms, inparticular the dimer bonds parallel to the surface plane and also thesilicon back bonds can be seen. Using a stable passivated tip obtainedfollowing the method described above, a small defect-free area can beimaged in STM as in FIG. 19B. The feedback loop is then switched off,the bias set to 0V and the scanner switched to AFM scanning mode. Thetip position defined by the STM imaging set points before switching offthe feedback loop is taken as a reference, that is, Z=Å. FIG. 2c-h showsa series of AFM frequency shift maps at different elevations. Sincethese images are taken in constant height mode, more repulsivetip-sample interactions appear brighter. In this example, substantialcontrast starts to be visible at Z=−3.0 Å (FIG. 19C) where we clearlysee single atoms appearing as a bright protrusion and organized in aclear 2×1 reconstruction. As the tip is brought closer to the surface by0.2 Å in FIG. 19C, the signal to noise is improved and the atomiccontrast is clearer. Superimposing the surface model to the AFM imageallows us to further highlight that, at this tip-sample distance, onlythe hydrogenated silicon atoms are visible.

However, as the tip-sample distance is decreased, bright and sharpbond-like features appear between atoms of a dimer as clearly seen inFIG. 19E at Z=−3.4 Å. These features appear to be due to the silicondimer bonds. In addition, one notices features consistent with theback-bonds between dimer and second layer silicon atoms in accordancewith the surface model in FIG. 19A. Although this surface was previouslyinvestigated both experimentally (32,33) and theoretically (34,35) usingNC-AFM, the evolution toward images consistent with the known bondstructure as reported here is unprecedented.

Interestingly, when decreasing the tip elevation to Z=−3.6 Å in FIG.19F, it is seen that in addition to the intra-silicon contrastenhancement, new sharp features appear in the inter-silicon dimer rowregion between two hydrogen atoms. These appear more pronounced in FIGS.19G and 19H. Unlike what appears to be the bond contrast correspondingto the silicon dimer bond, the feature in the inter-dimer region doesnot correspond to a real chemical bond as can be understood from theball and stick model of the silicon surface (FIG. 19H). Moreover, themodel shows that this AFM feature also does not correspond to theposition of third-layer silicon atoms.

Notably, tip and substrate geometries are altered during imaging,especially at very small tip heights. To determine the unperturbedsubstrate structure, it is necessary to create a candidate structure andsubject that to a simulated imaging process at a range of tip heights.Simulations done in this way capture force-induced alterations ofstructure and thereby result in modelled images that can be comparedwith experiment.

To simulate AFM images, it is important to choose a correct level oftheory to properly consider the necessary undergoing physics andchemistry while keeping the calculations tractable. In addition, theatomistic definition of tip and substrate is a requirement in manycases. Among first-principle frameworks, DFT is the first choice,especially when dispersion correction has been considered to include thesmall long-range forces at large tip-sample separations. Unfortunately,DFT is computationally expensive for many systems, especially thosewhere imaging must be done for a bulk structure, not only a molecule.Here DFTB is used, which at a lower computational cost can provideresults comparable with DFT using traditional semi-local functionals forthe silicon-based systems (36).

The modelled system is shown in FIG. 20A. The pyramid-like reconstructedstructure considered for the tip ends with a tilted passivated silicondimer so that the apex is a hydrogen atom. This tip consists of siliconand hydrogen atoms as an approximation to the passivated AFM tip used inthis work. Similar model tips, called ‘dimer tip’, have been previouslystudied in the literature and satisfactory results have been reported(13,37,38). Here we placed more bulk structures at the base of the tipwhich, along with the hydrogen passivation of the silicon danglingbonds, result in higher stability. This structure can be geometricallyoptimized by various ab initio methods without the need to freeze thebase atoms which leads to an unstrained structure increasing thefidelity of the forces read on the tip atoms.

For the substrate, a super-cell consisting of a H—Si(100)-2×1 siliconslab containing three dimer rows with six dimers per row is used. Theslab consists of 10 silicon layers with the bottom one terminated withhydrogen atoms. The lowermost two silicon layers of the slab and theuppermost silicon atoms of the tip, along with their passivatinghydrogens, are fixed to allow the constant height criteria of AFM. Therest of the atoms are relaxed to a force threshold of 0.02 eV/A.

Initially, the tip has been placed at different elevations with respectto the substrate. The height is measured as the distance between thetopmost substrate atom and the lowermost tip atom. The forces on the tipatoms are read after the relaxation, then the tip is shifted by 0.1 Å inx- or y-direction for the next point calculation. The scans at each tipelevation are performed from one hydrogen atom, to the next equivalenthydrogen atoms along and across the dimer rows. At each elevation, therewere about 3,000 geometry optimization calculations with the resultsshown in FIG. 20B.

In good agreement with the experimental results, it is seen that athigher tip elevations, the dimer atoms appear as bright protrusions. Asthe tip approaches the surface, the atomic features start to dim whilefeatures in the silicon dimer bond region start to appear. Finally, atvery low elevation (0.5 Å), an apparent dimer bond and its constituentatoms are indistinguishable. In addition, it is noticed that the falsebond feature in the interdimer region appearing at lower tip elevationimages, similar to the experimental results.

Next, the effect of tip flexibility in the imaging of this surface andalso in enhancing the AFM topographic feature registered betweenadjacent dimers in different dimer rows is discussed, where it is knownwith certainty that there is no hydrogen bond or covalent bond.Atomistic modelling can provide useful insights in this regard. In thesimulations, tip flexibility plays a significant role. That role isresolved by restricting some structural relaxations. Additional sets ofsimulations are performed by fixing all of the tip atoms while lettingthe surface atoms of the substrate relax as before. The results areshown in FIG. 20C where one sees a thicker feature in the dimer bondregion and bright atomic protrusions even at low tip elevation, which isdifferent from the experiment. This is due to the lower freedom ofmovement for the rigid tip which causes stronger forces to be read onit. As a result, the bond contrast is somewhat lowered. Nevertheless, itshows what appears to be a bond contrast where we know the Si—Si bond islocated. This shows that although the tip flexibility is not necessaryto observe a chemical bond-like contrast over the dimer, it certainlyenhances such contrast. In addition, the tip flexibility makes theinter-dimer contrast more visible. This is reminiscent of the debate inthe literature about the role of the CO molecule flexibility to accountfor contrast due to bonds within molecules and between molecules(9,10,16,17,22).

To highlight the difference in the high-resolution AFM images betweenfeatures corresponding to real chemical bonds and those appearing in thesilicon inter-dimer region, additional calculation results are presentedusing two different systems. The calculations are done at a very low tipelevation. In these cases, the tip is flexible, but the substrate isfrozen. In the first system, the substrate is as before with the atomsfrozen at the relaxed positions. In the second system, the dimerhydrogens are bent slightly, while keeping their bond length at theequilibrium value (that is, 1.5 Å) so that the distances between dimerand inter-dimer hydrogens are reversed with respect to the equilibriumcase, as shown in FIGS. 21A and 21B. This gives us the opportunity toinvestigate whether the AFM chemical bond contrast is dominantly due tothe Si—Si bonds, or it is more a consequence of the flexible tipscanning over closely spaced H atoms.

In the first system, what appears to be dimer bonds are visible asbefore, although some contrast is compromised due to the rigidity of thesubstrate. Interestingly, in the second system, the image contrast isstill much sharper above the Si—Si dimer bond, despite the H—H distancebeing shorter in the inter-dimer region than over the dimer. If thefeature seen in the dimer bond region were an artifact due to aconvolution of a flexible tip with the H atoms attached to the dimer,one would see the dimer bond-like feature be diminished upon separatingthe H atoms as was done. Moreover, a stronger feature would be seen inthe inter-row region than above the dimer, which is clearly not thecase. This provides shows that H—H orbital overlap is not the maincontributor to the intradimer bond features seen in the experiment. Wenote again at this point that, unlike other surface parallel bondedatoms imaged to date, these are σ bonded and not a π bonded atoms.

Furthermore, the results from FIG. 21B help explain the origin of theback-bond features seen in the experimental and theoretical AFM imagesat lower elevations. As shown in this figure, the distance between theintra-dimer hydrogens is 3.5 Å, which is less than the 3.9 Å betweenadjacent H atoms on different dimer rows. Yet, it is possible to stillsee much more prominent image features where the silicon back-bonds areexpected (FIG. 19A). It appears, within the calculations, that thesilicon atoms and possibly the Si—Si σ bonds are the major contributorfor the bond feature contrast corresponding to the back-bonds, and thatthe H—H overlap plays a minor role here.

To summarize, the present inventions establishes that ahydrogen-passivated tip can be reliably prepared and identified. Thispassivated tip is used to image the H—Si(100)-2×1 surface. Using aDFTB-based approach to AFM simulation, the evolution of AFM images atdifferent tip elevations are successfully reproduced. It is shown thattip flexibility enhances and sharpens the appearance in AFM images ofwhat are known to be true covalent bonds. Moreover, it is shown thatnon-bonded atoms in close proximity can appear bonded, and that falseimpression is enhanced by tip flexibility.

References cited herein are incorporated by reference to the same extentas if each reference was individually and explicitly incorporated byreference.

As a person skilled in the art will recognize from the previous detaileddescription and from the figures and claims, modifications and changescan be made to the preferred embodiments of the invention withoutdeparting from the scope of this invention defined in the followingclaims.

1. A multiple-atom germanium quantum dot comprising: a first pluralityof dangling bonds on an otherwise H-terminated germanium latticesurface, each of said first plurality of dangling bonds having one ofthree ionization states of +1, 0 or −1 and corresponding respectively to0, 1, or 2 electrons in a dangling bond state; said first plurality ofdangling bonds being as close together as the germanium lattice allowsand having the dangling bond states energetically in the germanium bandgap with selective control of the ionization state of one of said firstplurality of dangling bonds.
 2. The dot of claim 1 wherein the pluralityof dangling bonds is three to ten dangling bonds.
 3. The dot of claim 1wherein the plurality of dangling bonds is more than ten dangling bonds.4. The dot of claim 1 wherein said first plurality of dangling bonds arelinear.
 5. The dot of claim 1 wherein said first plurality of danglingbonds are on adjacent H-terminated germanium atoms.
 6. The dot of claim1 wherein there is at least one H-terminated germanium atom intermediatebetween said first plurality of dangling bonds.
 7. The dot of claim 1wherein said plurality of dangling bonds form a wire with a perturbationat a first end communicated to an opposing end to the first end.
 8. Thedot of claim 1 further comprising an input and an output.
 9. The dot ofclaim 8 wherein the input and an output form a gate.
 10. The dot ofclaim 9 wherein the gate is an OR gate.
 11. The dot of claim 1 furthercomprising a second plurality of dangling bonds on an otherwiseH-terminated germanium lattice surface, each of said second plurality ofdangling bonds having one of three ionization states of +1, 0, or −1 andcorresponding respectively to 0, 1, or 2 electrons in a dangling bondstate, said second plurality of dangling bonds being as close togetheras the germanium lattice allows and having the dangling bond statesenergetically in the germanium band gap with selective control of theionization state of one of said second plurality of dangling bonds. 12.The dot of claim 11 wherein the second plurality of dangling bondsincludes 2 to 10,000 dangling bonds.
 13. The dot of claim 11 wherein thesecond plurality of dangling bonds is positioned parallel orperpendicular to the first plurality of dangling bonds.
 14. The dot ofclaim 11 wherein the second plurality of dangling bonds is positioned atan angle of 120° to the first plurality of dangling bonds.
 15. The dotof claim 11 wherein the first plurality of dangling bonds and thesecond.
 16. The dot of claim 11 further comprising an AFM tip as aninput and a third plurality of dangling bonds, wherein the first,second, and third pluralities of dangling bonds form a Y-shape on theH-terminated germanium surface.
 17. The dot of claim 16 wherein the AMFtip selectively adds or subtracts an electron or a hydrogen atom. 18.The dot of claim 11 further comprising an electrostatic bias positionedat an end of the dot to allow the dot to return to a state ofequilibrium.
 19. The dot of claim 11 wherein the dot is capable ofperforming clocking function on the order of every <10⁻¹³ seconds. 20.An electronic device comprising: at least one multiple-atom germaniumquantum dot of claim 1; and at least contact in electronic communicationwith the at least one multiple-atom germanium quantum dot.